The euro came off from its early lows against the other major currencies in European deals on Tuesday, as a media report indicated that Greek Prime Minister Alexis Tsipras is examining the latest aid proposal made by European Commission President Jean-Claude Juncker.

According to Greek daily Kathimerini, Greek PM's office intimated Brussels that they are working on new proposal of Junker which included debt relief in October and changes in the EKAS supplement (for low-income Greeks)

The offer, which was published on Sunday, requires the Greek PM to pledge "Yes" campaign for the planned July 5 referendum, while conveying a written acceptance of the proposed plan to the lenders today.

Meanwhile, the European stocks are trading in a negative territory, amid uncertainty about the future of Greece in euro area, after Greece said that it won't make the 1.6 billion euro debt payment to the International Monetary Fund due today.

In economic front, the flash data from Eurostat showed that Eurozone inflation slowed slightly in June after accelerating in May.

Inflation eased to 0.2 percent in June, in line with forecast, from 0.3 percent in the prior month.

Another report from Eurostat showed that the unemployment rate remained unchanged at 11.1 percent in May. This was the lowest rate recorded in the euro area since March 2012. It came in line with expectations.

The currency drifted lower in the Asian session, due to Greece debt default fears.

The euro bounced off to 1.1205 against the greenback, 137.24 against the yen and 0.7126 against the pound, from its early lows of 1.1133, 135.87 and 0.7081, respectively. The euro ended Monday's trading at 1.1234 against the greenback, 137.65 against the yen and 0.7139 against the pound.

The euro was trading at 1.0414 against the franc, moving away from its previous low of 1.0371. The pair was valued at 1.0391 at yesterday's close.

Looking ahead, Canada GDP for April, U.S. S&P/Case-Shiller home price index for April, U.S. Chicago PMI and U.S. consumer confidence, both for June, are set to be published in the New York session.

At 7:00 am ET, Bank of England Chief Economist Andy Haldane is expected to speak at the Open University in London.

An hour later, European Central Bank Governing Council member Ewald Nowotny will give a keynote speech at "Raiffeisen Bank International-Summer Talk" in Vienna.

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